Multiple order pole pure lag rational function approximations for unsteady aerodynamics

Abstract

Most existing rational function approximations for the time domain representation of unsteady generalized airloads lead to an ill-conditioned system dynamic matrix in the presence of closely spaced poles. A new class of multiple order pole pure lag rational function approximations (RFA) is presented in this article to overcome this problem. The present class of approximation s is developed as a consistent generalization of an existing simple pole pure lag RFA while preserving the resulting state vector dimension. A nonlinear nongradient optimization technique is used for the computation of the lag poles in the approximation. The structure of the proposed class of approximations preserves the pure lag form, thus allowing for specific physical interpretations of the individual terms in the approximation and renders the subsequent optimization problem simpler, in that fewer constraints need to be imposed during the optimization process. Furthermore, the new class of approximations leads to substantial reduction in computational costs for optimization for a given fit accuracy, in comparison to existing simple pole approximations. Results are presented for the case of a typical delta wing fighter aircraft configuration.